Subgroups — C₁₉×#32720 #18038679

Order 4864.

890 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₉×#2856	C₂	1	1	yes	maximal, characteristic
2	C₁₉×#2855	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₉×#2099	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₉×#2096	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₉×#2065	C₂	1	2	yes	maximal, complemented
6	C₁₉×#2055	C₂	1	2	yes	maximal, complemented
7	C₁₉×#2041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₉×#2034	C₂	1	2	yes	maximal, complemented
9	C₁₉×#2014	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₉×#2000	C₂	1	2	yes	maximal, complemented
11	C₁₉×#1797	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×SD₁₆×C₁₉	C₂²	1	2	yes	—
13	C₂×C₁₉×#127	C₂²	1	1	yes	characteristic
14	C₂×C₁₉×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₁₉×#121	—	2	1	no	—
16	C₂×C₁₉×#121	—	2	1	no	—
17	C₂×C₁₉×#121	C₂²	1	2	yes	—
18	C₂²×C₄²×C₁₉	C₂²	1	1	yes	characteristic
19	C₂×C₁₉×#106	C₂²	1	2	yes	—
20	C₂×C₁₉×C₄⋊C₈	C₂²	1	2	yes	—
21	C₂×C₁₉×#103	C₂²	1	2	yes	—
22	C₂×C₁₉×#102	C₂²	1	2	yes	—
23	C₂×C₁₉×#102	C₂²	1	2	yes	—
24	C₂×C₁₉×#102	C₂²	1	2	yes	—
25	C₂×C₁₉×C₂²⋊C₈	C₂²	1	2	yes	—
26	C₁₉×#391	C₂²	1	1	yes	characteristic
27	C₁₉×#391	C₂²	1	1	yes	characteristic
28	C₁₉×#390	—	2	1	no	—
29	C₁₉×#390	—	2	1	no	—
30	C₁₉×#390	C₂²	1	2	yes	—
31	C₁₉×#389	C₂²	1	1	yes	characteristic
32	C₁₉×#389	C₂²	1	1	yes	characteristic
33	C₁₉×#387	—	2	1	no	—
34	C₁₉×#387	—	2	1	no	—
35	C₁₉×#385	—	2	1	no	—
36	C₁₉×#384	C₂²	1	1	yes	characteristic
37	C₁₉×#381	—	2	1	no	—
38	C₁₉×#380	C₂²	1	1	yes	characteristic
39	C₁₉×#340	C₂²	1	2	yes	—
40	C₁₉×#340	C₂²	1	2	yes	—
41	C₁₉×#336	C₂²	1	1	yes	characteristic
42	C₁₉×#336	C₂²	1	1	yes	characteristic
43	C₂²×Q₈×C₁₉	C₂³	1	1	yes	characteristic
44	C₂²×D₄×C₁₉	—	2	2	no	—
45	C₂²×D₄×C₁₉	—	2	1	no	—
46	C₂²×D₄×C₁₉	—	2	1	no	—
47	C₂²×D₄×C₁₉	C₂³	1	2	yes	—
48	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₁₉	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₁₉	C₂³	1	1	yes	characteristic
51	C₂×SD₁₆×C₁₉	—	4	2	no	—
52	C₂×SD₁₆×C₁₉	—	4	2	no	—
53	C₂×SD₁₆×C₁₉	—	4	2	no	—
54	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₉	C₂³	1	2	yes	—
56	C₁₉×#127	—	4	2	no	—
57	C₁₉×C₂²⋊Q₈	—	4	2	no	—
58	C₁₉×#121	—	4	2	no	—
59	C₁₉×#121	—	4	2	no	—
60	C₁₉×#121	—	4	4	no	—
61	C₁₉×#121	—	4	4	no	—
62	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
63	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
64	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
65	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
66	C₂×C₄⋊C₄×C₁₉	—	2	1	no	—
67	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₁₉	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₁₉	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₁₉	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₁₉	—	2	2	no	—
76	C₂×C₄²×C₁₉	—	4	2	no	—
77	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₁₉	D₄	1	1	yes	characteristic
79	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₁₉	C₂³	1	1	yes	characteristic
81	C₁₉×#106	—	4	2	no	—
82	C₁₉×C₄⋊C₈	—	4	2	no	—
83	C₁₉×#103	—	4	2	no	—
84	C₁₉×#102	—	4	2	no	—
85	C₁₉×#102	—	4	2	no	—
86	C₁₉×#102	—	4	2	no	—
87	C₁₉×C₂²⋊C₈	—	4	2	no	—
88	C₁₉×#95	—	2	1	no	—
89	C₁₉×#95	—	2	1	no	—
90	C₁₉×#95	—	2	1	no	—
91	C₁₉×#95	—	2	1	no	—
92	C₁₉×#95	—	2	1	no	—
93	C₁₉×#95	—	2	1	no	—
94	C₁₉×#95	—	2	1	no	—
95	C₂⁴×C₁₉	—	2	2	no	—
96	C₂⁴×C₁₉	C₂×D₄	1	1	yes	characteristic
97	C₂×Q₈×C₁₉	—	2	2	no	—
98	C₂×Q₈×C₁₉	—	2	1	no	—
99	C₂×Q₈×C₁₉	—	2	2	no	—
100	C₂×Q₈×C₁₉	—	2	1	no	—
101	C₂×D₄×C₁₉	—	2	2	no	—
102	C₂×D₄×C₁₉	—	2	2	no	—
103	C₂×D₄×C₁₉	—	2	2	no	—
104	C₂×D₄×C₁₉	—	2	2	no	—
105	C₂×D₄×C₁₉	—	2	2	no	—
106	C₂×D₄×C₁₉	—	2	2	no	—
107	C₂×D₄×C₁₉	—	4	2	no	—
108	C₂×D₄×C₁₉	—	4	2	no	—
109	C₂×D₄×C₁₉	—	4	2	no	—
110	C₂×D₄×C₁₉	—	4	2	no	—
111	C₂×D₄×C₁₉	—	4	4	no	—
112	C₂×D₄×C₁₉	—	4	4	no	—
113	C₂×D₄×C₁₉	—	4	4	no	—
114	C₂×D₄×C₁₉	—	4	2	no	—
115	C₂×D₄×C₁₉	—	4	2	no	—
116	C₂²×C₄×C₁₉	—	2	2	no	—
117	C₂²×C₄×C₁₉	—	2	2	no	—
118	C₂²×C₄×C₁₉	—	2	2	no	—
119	C₂²×C₄×C₁₉	—	2	1	no	—
120	C₂²×C₄×C₁₉	—	2	1	no	—
121	C₂²×C₄×C₁₉	—	2	2	no	—
122	C₂²×C₄×C₁₉	—	2	1	no	—
123	C₂²×C₄×C₁₉	—	2	1	no	—
124	C₂²×C₄×C₁₉	—	2	1	no	—
125	C₂²×C₄×C₁₉	—	2	1	no	—
126	C₂²×C₄×C₁₉	—	4	1	no	—
127	C₂²×C₄×C₁₉	—	4	1	no	—
128	C₂²×C₄×C₁₉	—	4	1	no	—
129	C₂²×C₄×C₁₉	—	4	1	no	—
130	C₂²×C₄×C₁₉	SD₁₆	1	4	yes	complemented
131	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₉	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₉	C₂⁴	1	1	yes	characteristic
137	SD₁₆×C₁₉	—	4	8	no	—
138	C₂×C₈×C₁₉	—	2	2	no	—
139	C₂×C₈×C₁₉	—	2	2	no	—
140	C₂×C₈×C₁₉	—	2	2	no	—
141	C₂×C₈×C₁₉	—	2	2	no	—
142	C₂×C₈×C₁₉	—	2	2	no	—
143	C₂×C₈×C₁₉	—	2	2	no	—
144	C₄⋊C₄×C₁₉	—	2	2	no	—
145	C₄⋊C₄×C₁₉	—	2	2	no	—
146	C₄⋊C₄×C₁₉	—	2	2	no	—
147	C₄⋊C₄×C₁₉	—	2	1	no	—
148	C₄⋊C₄×C₁₉	—	2	2	no	—
149	C₄⋊C₄×C₁₉	—	2	1	no	—
150	C₄⋊C₄×C₁₉	—	4	2	no	—
151	C₄⋊C₄×C₁₉	—	4	2	no	—
152	C₄⋊C₄×C₁₉	—	4	2	no	—
153	C₄⋊C₄×C₁₉	—	4	2	no	—
154	C₄⋊C₄×C₁₉	—	4	2	no	—
155	C₂²⋊C₄×C₁₉	—	4	4	no	—
156	C₂²⋊C₄×C₁₉	—	4	4	no	—
157	C₂²⋊C₄×C₁₉	—	4	2	no	—
158	C₂²⋊C₄×C₁₉	—	4	2	no	—
159	C₂²⋊C₄×C₁₉	—	4	4	no	—
160	C₄²×C₁₉	—	2	2	no	—
161	C₄²×C₁₉	—	2	2	no	—
162	C₄²×C₁₉	—	4	1	no	—
163	C₄²×C₁₉	—	4	1	no	—
164	#32720	C₁₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂³×C₁₉	—	2	1	no	—
166	C₂³×C₁₉	—	2	1	no	—
167	C₂³×C₁₉	—	2	1	no	—
168	C₂³×C₁₉	—	2	1	no	—
169	C₂³×C₁₉	—	2	1	no	—
170	C₂³×C₁₉	—	2	1	no	—
171	C₂³×C₁₉	—	4	2	no	—
172	C₂³×C₁₉	—	4	2	no	—
173	C₂³×C₁₉	—	4	2	no	—
174	C₂³×C₁₉	—	4	2	no	—
175	C₂³×C₁₉	—	4	2	no	—
176	C₂³×C₁₉	—	4	2	no	—
177	C₂³×C₁₉	—	4	2	no	—
178	C₂³×C₁₉	C₂×SD₁₆	1	2	yes	—
179	C₂³×C₁₉	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₁₉	—	4	2	no	—
181	Q₈×C₁₉	—	4	2	no	—
182	D₄×C₁₉	—	4	2	no	—
183	D₄×C₁₉	—	4	2	no	—
184	D₄×C₁₉	—	4	2	no	—
185	D₄×C₁₉	—	4	2	no	—
186	D₄×C₁₉	—	8	4	no	—
187	D₄×C₁₉	—	8	4	no	—
188	D₄×C₁₉	—	8	8	no	—
189	C₂×C₄×C₁₉	—	2	1	no	—
190	C₂×C₄×C₁₉	—	2	1	no	—
191	C₂×C₄×C₁₉	—	2	1	no	—
192	C₂×C₄×C₁₉	—	2	1	no	—
193	C₂×C₄×C₁₉	—	2	1	no	—
194	C₂×C₄×C₁₉	—	2	1	no	—
195	C₂×C₄×C₁₉	—	2	1	no	—
196	C₂×C₄×C₁₉	—	2	1	no	—
197	C₂×C₄×C₁₉	—	2	1	no	—
198	C₂×C₄×C₁₉	—	2	1	no	—
199	C₂×C₄×C₁₉	—	2	1	no	—
200	C₂×C₄×C₁₉	—	2	1	no	—
201	C₂×C₄×C₁₉	—	4	4	no	—
202	C₂×C₄×C₁₉	—	4	4	no	—
203	C₂×C₄×C₁₉	—	4	2	no	—
204	C₂×C₄×C₁₉	—	4	2	no	—
205	C₂×C₄×C₁₉	—	4	1	no	—
206	C₂×C₄×C₁₉	—	4	1	no	—
207	C₂×C₄×C₁₉	—	4	2	no	—
208	C₂×C₄×C₁₉	—	4	1	no	—
209	C₂×C₄×C₁₉	—	4	1	no	—
210	C₂×C₄×C₁₉	—	4	1	no	—
211	C₂×C₄×C₁₉	—	4	1	no	—
212	C₂×C₄×C₁₉	—	4	2	no	—
213	C₂×C₄×C₁₉	—	4	2	no	—
214	C₂×C₄×C₁₉	—	4	1	no	—
215	C₂×C₄×C₁₉	—	4	1	no	—
216	C₂×C₄×C₁₉	—	4	1	no	—
217	C₂×C₄×C₁₉	—	4	1	no	—
218	C₂×C₄×C₁₉	—	4	1	no	—
219	C₂×C₄×C₁₉	—	4	1	no	—
220	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
221	C₂×C₄×C₁₉	C₂×SD₁₆	1	2	yes	—
222	C₂×C₄×C₁₉	AGL(1,ℤ/8)	1	2	yes	—
223	C₂×C₄×C₁₉	H(5,𝔽₂)	1	1	yes	characteristic
224	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
225	C₂×C₄×C₁₉	H(5,𝔽₂)	1	2	yes	—
226	C₂×C₄×C₁₉	2₋¹⁺⁴	1	1	yes	characteristic
227	C₈×C₁₉	—	4	2	no	—
228	C₈×C₁₉	—	4	2	no	—
229	#2856	C₂×C₁₉	1	1	yes	characteristic
230	#2855	C₂×C₁₉	1	1	yes	characteristic, complemented
231	#2099	C₂×C₁₉	1	1	yes	characteristic, complemented
232	#2096	C₂×C₁₉	1	1	yes	characteristic, complemented
233	#2065	C₂×C₁₉	1	2	yes	complemented
234	#2055	C₂×C₁₉	1	2	yes	complemented
235	#2041	C₂×C₁₉	1	1	yes	characteristic, complemented
236	#2034	C₂×C₁₉	1	2	yes	complemented
237	#2014	C₂×C₁₉	1	1	yes	characteristic, complemented
238	#2000	C₂×C₁₉	1	2	yes	complemented
239	#1797	C₂×C₁₉	1	1	yes	characteristic, complemented
240	C₂²×C₁₉	—	2	2	no	—
241	C₂²×C₁₉	—	2	2	no	—
242	C₂²×C₁₉	—	2	2	no	—
243	C₂²×C₁₉	—	4	1	no	—
244	C₂²×C₁₉	—	4	1	no	—
245	C₂²×C₁₉	—	4	1	no	—
246	C₂²×C₁₉	—	4	1	no	—
247	C₂²×C₁₉	—	8	2	no	—
248	C₂²×C₁₉	—	8	2	no	—
249	C₂²×C₁₉	—	8	2	no	—
250	C₂²×C₁₉	—	8	2	no	—
251	C₂²×C₁₉	—	8	2	no	—
252	C₂²×C₁₉	—	8	2	no	—
253	C₂²×C₁₉	—	8	2	no	—
254	C₂²×C₁₉	#534	1	1	yes	characteristic
255	C₂²×C₁₉	#535	1	1	yes	characteristic
256	C₂²×C₁₉	#537	1	1	yes	characteristic
257	C₂²×C₁₉	C₂²×SD₁₆	1	1	yes	characteristic
258	C₂²×C₁₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
259	C₂²×C₁₉	#575	1	1	yes	characteristic
260	C₂²×C₁₉	#575	1	1	yes	characteristic
261	C₄×C₁₉	—	2	2	no	—
262	C₄×C₁₉	—	2	2	no	—
263	C₄×C₁₉	—	2	2	no	—
264	C₄×C₁₉	—	4	1	no	—
265	C₄×C₁₉	—	4	1	no	—
266	C₄×C₁₉	—	8	1	no	—
267	C₄×C₁₉	—	8	2	no	—
268	C₄×C₁₉	—	8	1	no	—
269	C₄×C₁₉	—	8	1	no	—
270	C₄×C₁₉	—	8	1	no	—
271	C₄×C₁₉	#560	1	2	yes	—
272	C₄×C₁₉	#562	1	2	yes	—
273	C₂²×SD₁₆	C₂²×C₁₉	1	2	yes	—
274	C₂×#127	C₂²×C₁₉	1	1	yes	characteristic
275	C₂×C₂²⋊Q₈	C₂²×C₁₉	1	1	yes	characteristic
276	C₂×#121	—	2	1	no	—
277	C₂×#121	—	2	1	no	—
278	C₂×#121	C₂²×C₁₉	1	2	yes	—
279	C₂²×C₄²	C₂²×C₁₉	1	1	yes	characteristic
280	C₂×#106	C₂²×C₁₉	1	2	yes	—
281	C₂×C₄⋊C₈	C₂²×C₁₉	1	2	yes	—
282	C₂×#103	C₂²×C₁₉	1	2	yes	—
283	C₂×#102	C₂²×C₁₉	1	2	yes	—
284	C₂×#102	C₂²×C₁₉	1	2	yes	—
285	C₂×#102	C₂²×C₁₉	1	2	yes	—
286	C₂×C₂²⋊C₈	C₂²×C₁₉	1	2	yes	—
287	#391	C₂²×C₁₉	1	1	yes	characteristic
288	#391	C₂²×C₁₉	1	1	yes	characteristic
289	#390	—	2	1	no	—
290	#390	—	2	1	no	—
291	#390	C₂²×C₁₉	1	2	yes	—
292	#389	C₂²×C₁₉	1	1	yes	characteristic
293	#389	C₂²×C₁₉	1	1	yes	characteristic
294	#387	—	2	1	no	—
295	#387	—	2	1	no	—
296	#385	—	2	1	no	—
297	#384	C₂²×C₁₉	1	1	yes	characteristic
298	#381	—	2	1	no	—
299	#380	C₂²×C₁₉	1	1	yes	characteristic
300	#340	C₂²×C₁₉	1	2	yes	—
301	#340	C₂²×C₁₉	1	2	yes	—
302	#336	C₂²×C₁₉	1	1	yes	characteristic
303	#336	C₂²×C₁₉	1	1	yes	characteristic
304	C₂×C₁₉	—	4	2	no	—
305	C₂×C₁₉	—	16	2	no	—
306	C₂×C₁₉	#2813	1	1	yes	characteristic
307	C₂×C₁₉	#3187	1	1	yes	characteristic
308	C₂×C₁₉	#3194	1	1	yes	characteristic
309	C₂×C₁₉	#3208	1	1	yes	characteristic
310	C₂×C₁₉	#3219	1	1	yes	characteristic
311	C₂×C₁₉	#3246	1	1	yes	characteristic
312	C₂×C₁₉	#3251	1	1	yes	characteristic
313	C₂²×Q₈	C₂³×C₁₉	1	1	yes	characteristic
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	—	2	1	no	—
316	C₂²×D₄	—	2	1	no	—
317	C₂²×D₄	C₂³×C₁₉	1	2	yes	—
318	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
319	C₂³×C₄	D₄×C₁₉	1	1	yes	characteristic
320	C₂³×C₄	C₂³×C₁₉	1	1	yes	characteristic
321	C₂×SD₁₆	—	4	2	no	—
322	C₂×SD₁₆	—	4	2	no	—
323	C₂×SD₁₆	—	4	2	no	—
324	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
325	C₂²×C₈	C₂³×C₁₉	1	2	yes	—
326	#127	—	4	2	no	—
327	C₂²⋊Q₈	—	4	2	no	—
328	#121	—	4	2	no	—
329	#121	—	4	2	no	—
330	#121	—	4	4	no	—
331	#121	—	4	4	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	—	2	1	no	—
337	C₂×C₄⋊C₄	C₂³×C₁₉	1	2	yes	—
338	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
340	C₂×C₄⋊C₄	C₂³×C₁₉	1	1	yes	characteristic
341	C₂×C₂²⋊C₄	—	2	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	2	2	no	—
344	C₂×C₂²⋊C₄	—	2	2	no	—
345	C₂×C₂²⋊C₄	—	2	2	no	—
346	C₂×C₄²	—	4	2	no	—
347	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
348	C₂×C₄²	D₄×C₁₉	1	1	yes	characteristic
349	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
350	C₂×C₄²	C₂³×C₁₉	1	1	yes	characteristic
351	#106	—	4	2	no	—
352	C₄⋊C₈	—	4	2	no	—
353	#103	—	4	2	no	—
354	#102	—	4	2	no	—
355	#102	—	4	2	no	—
356	#102	—	4	2	no	—
357	C₂²⋊C₈	—	4	2	no	—
358	#95	—	2	1	no	—
359	#95	—	2	1	no	—
360	#95	—	2	1	no	—
361	#95	—	2	1	no	—
362	#95	—	2	1	no	—
363	#95	—	2	1	no	—
364	#95	—	2	1	no	—
365	C₁₉	#32720	1	1	yes	characteristic, direct product factor, Sylow
366	C₂⁴	—	2	2	no	—
367	C₂⁴	C₂×D₄×C₁₉	1	1	yes	characteristic
368	C₂×Q₈	—	2	2	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	1	no	—
371	C₂×Q₈	—	2	1	no	—
372	C₂×D₄	—	2	2	no	—
373	C₂×D₄	—	2	2	no	—
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	4	2	no	—
379	C₂×D₄	—	4	2	no	—
380	C₂×D₄	—	4	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	2	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂²×C₄	—	2	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	2	no	—
397	C₂²×C₄	—	4	1	no	—
398	C₂²×C₄	—	4	1	no	—
399	C₂²×C₄	—	4	1	no	—
400	C₂²×C₄	—	4	1	no	—
401	C₂²×C₄	SD₁₆×C₁₉	1	4	yes	complemented
402	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
406	C₂²×C₄	C₂×D₄×C₁₉	1	1	yes	characteristic
407	C₂²×C₄	C₂⁴×C₁₉	1	1	yes	characteristic
408	SD₁₆	—	4	8	no	—
409	C₂×C₈	—	2	2	no	—
410	C₂×C₈	—	2	2	no	—
411	C₂×C₈	—	2	2	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	4	4	no	—
427	C₂²⋊C₄	—	4	4	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	4	2	no	—
430	C₂²⋊C₄	—	4	4	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	2	no	—
433	C₄²	—	4	1	no	—
434	C₄²	—	4	1	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	2	no	—
446	C₂³	—	4	2	no	—
447	C₂³	—	4	2	no	—
448	C₂³	C₂×SD₁₆×C₁₉	1	2	yes	—
449	C₂³	C₂²×D₄×C₁₉	1	1	yes	characteristic
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	D₄	—	4	2	no	—
453	D₄	—	4	2	no	—
454	D₄	—	4	2	no	—
455	D₄	—	4	2	no	—
456	D₄	—	8	4	no	—
457	D₄	—	8	4	no	—
458	D₄	—	8	8	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	4	4	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
491	C₂×C₄	C₂×SD₁₆×C₁₉	1	2	yes	—
492	C₂×C₄	C₁₉×AGL(1,ℤ/8)	1	2	yes	—
493	C₂×C₄	C₁₉×H(5,𝔽₂)	1	1	yes	characteristic
494	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
495	C₂×C₄	C₁₉×H(5,𝔽₂)	1	2	yes	—
496	C₂×C₄	C₁₉×2₋¹⁺⁴	1	1	yes	characteristic
497	C₈	—	4	2	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	2	2	no	—
500	C₂²	—	2	2	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	8	2	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	—	8	2	no	—
510	C₂²	—	8	2	no	—
511	C₂²	—	8	2	no	—
512	C₂²	—	8	2	no	—
513	C₂²	C₁₉×#534	1	1	yes	characteristic
514	C₂²	C₁₉×#535	1	1	yes	characteristic
515	C₂²	C₁₉×#537	1	1	yes	characteristic
516	C₂²	C₂²×SD₁₆×C₁₉	1	1	yes	characteristic
517	C₂²	C₂×C₁₉×AGL(1,ℤ/8)	1	1	yes	characteristic
518	C₂²	C₁₉×#575	1	1	yes	characteristic
519	C₂²	C₁₉×#575	1	1	yes	characteristic
520	C₄	—	2	2	no	—
521	C₄	—	2	2	no	—
522	C₄	—	2	2	no	—
523	C₄	—	4	1	no	—
524	C₄	—	4	1	no	—
525	C₄	—	8	1	no	—
526	C₄	—	8	2	no	—
527	C₄	—	8	1	no	—
528	C₄	—	8	1	no	—
529	C₄	—	8	1	no	—
530	C₄	C₁₉×#560	1	2	yes	—
531	C₄	C₁₉×#562	1	2	yes	—
532	C₂	—	4	2	no	—
533	C₂	—	16	2	no	—
534	C₂	C₁₉×#2813	1	1	yes	characteristic
535	C₂	C₁₉×#3187	1	1	yes	characteristic
536	C₂	C₁₉×#3194	1	1	yes	characteristic
537	C₂	C₁₉×#3208	1	1	yes	characteristic
538	C₂	C₁₉×#3219	1	1	yes	characteristic
539	C₂	C₁₉×#3246	1	1	yes	characteristic
540	C₂	C₁₉×#3251	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₉	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₉
prime radical	C₁₉×#2856	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₉ ◁ C₂²×C₄²×C₁₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₁₉×#2855	C₂	semidirect
3. C₁₉×#2099	C₂	semidirect
4. C₁₉×#2096	C₂	semidirect
5. C₁₉×#2065	C₂	semidirect
6. C₁₉×#2055	C₂	semidirect
7. C₁₉×#2041	C₂	semidirect
8. C₁₉×#2034	C₂	semidirect
9. C₁₉×#2014	C₂	semidirect
10. C₁₉×#2000	C₂	semidirect
11. C₁₉×#1797	C₂	semidirect
130. C₂²×C₄×C₁₉	SD₁₆	semidirect
164. #32720	C₁₉	direct (N × H)
230. #2855	C₂×C₁₉	semidirect
231. #2099	C₂×C₁₉	semidirect
232. #2096	C₂×C₁₉	semidirect
233. #2065	C₂×C₁₉	semidirect
234. #2055	C₂×C₁₉	semidirect
235. #2041	C₂×C₁₉	semidirect
236. #2034	C₂×C₁₉	semidirect
237. #2014	C₂×C₁₉	semidirect
238. #2000	C₂×C₁₉	semidirect
239. #1797	C₂×C₁₉	semidirect
365. C₁₉	#32720	direct (N × H)
401. C₂²×C₄	SD₁₆×C₁₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₉×#2856	2
C₁₉×#2855	2
C₁₉×#2099	2
C₁₉×#2096	2
C₁₉×#2065	2
C₁₉×#2055	2
C₁₉×#2041	2
C₁₉×#2034	2
C₁₉×#2014	2
C₁₉×#2000	2
C₁₉×#1797	2
#32720	19

Subgroups — C19×#32720 #18038679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₉×#32720 #18038679